Author

Date of Award

Degree Type

Degree Name

Department

Mathematics

First Advisor

Mireille Boutin

Committee Chair

Mireille Boutin

Committee Member 1

Gregery Buzzard

Committee Member 2

Nung Kwan Aaron Yip

Committee Member 3

Carol J. Boushey

Abstract

Managing the intake of a certain nutrient can be an effective treatment for some inherited metabolic disorders. An example of such dietary treatments is for phenylketonuria (PKU), for which patients must follow a low-phenylalanine diet for life. Some food databases provide the phenylalanine (Phe) content for a large number of unprocessed foods, and a limited number of composite foods; however, they are not exhaustive. As an attempt to complete this list, we introduce three mathematical approaches to estimate a bound for the Phe content based on the available nutritional information. The first approach is based on the statistical distribution of the Phe to protein ratios. To be precise, we propose the multipliers 20 and 65 to obtain a minimum bound and a maximum bound for the Phe content from the protein content. The second approach is based on two simple lemmas which apply to sweets with gelatin. Specifically, we show that simple arithmetic operations can be used to determine an amount of sweets that is guaranteed to contain less than 20 mg Phe. The third approach is based on numerical optimization. We use the ingredient list and the Nutrition Facts Label to set up a set of inequalities which we solve numerically. The first step of our solution provides estimates for the ingredient amounts. This can be viewed as an approximate inverse recipe method. Although these mathematical methods are primarily motivated by the problem of estimating the Phe content, they can also be applied to estimating the content of other nutrient. In particular, they could be used to complete missing values in current food composition databases.